F311_1CapStudyTemplate

7/27/2019 F311_1CapStudyTemplate

1/18

Study Date

Part Number

Operation

Sequence

Seq. Descr.

Department

Machine

Nominal Spec. Note:Use the examples below to help you decide how to input the nominal and specs.

+ Tol. or USL

- Tol. or LSL

Unitsnm

Typeb Note: Enter "b" or leave blank for bilateral tolerances. High-lite cell to activate pulldown.

Enter "u" for LSL bounded unilateral tolerances. High-lite cell to activate pulldown.

Multiplier1 Note: The multiplier and additive allow you to enter coded data below. Each

Additive0 data point is first multiplied by the multiplier and then the additive is

added to the result. If entering actual values, use the defaults (1 and 0).

Comments:

Force NormalYes Note: Enter "Y" to calculate capability indices based on a normal distribution.

Data Points

Piece # Value Actual Values

1 =

2 =

3 =

4 =

5 =

6 =

7 =

8 =

9 =

10 =11 =

12 =

13 =

14 =

15 =

16 =

17 =

18 =

19 =

20 =

21 =

22 =

23 =

24 =

25 =

26 =

27 =

28 =

29 =

30 =

31 =

32 =

33 =

34 =

35 =

36 =

37 =

38 =

39 =40 =

Nominal Spec. 24.536

+ Tol. or USL 0.05

- Tol. or LSL -0.05

Nominal Spec.

+ Tol. or USL 24.586

- Tol. or LSL 24.486

Nominal Spec.

+ Tol. or USL 586

- Tol. or LSL 486


2/18

JDWW Process Capability Study0

General Statistics: ( 0 data points, 3 pc subgroups ) Date of Study: 00Jan00

Minimum = 0.0000 Mean = 0.0000 Maximum = 0.0000

Lower Process Limit = Targeting = 0.0000 Upper Process Limit =

Lower Spec. Limit = -0.5000 Nominal = 0.0000 Upper Spec. Limit = 0.5000

Std. Dev = 1.000000 Skewness =

6 Sigma = Total Tol. = Kurtosis =

Process Capability Indices (using +/- 3 Sigma for Normal data):

Cp = 1.0000 Cpl = Z(LSL) =

Cr = Cpu = Z(USL) =

PPM (Total) = Cpk = 1.3300 Z(Min) = 0.0000

PPM or () will be under the LSL value of -0.5000

PPM or () will be over the USL value of 0.5000

The amount of variation is acceptable, 1.00 Cp. After adjusting the inherent capability, Cp, to 1.33, the

target error , 0.0000, is acceptable.

0

0.2

0.4

0.6

0.8

1

1.2

1 2

Averages are in control.

Xbar Control Chart

X bar

UCL

X barbar

LCL

SubGrp Size = 3

0

0.2

0.4

0.6

0.8

1

1.2

1 2

Ranges are in control.

Range Control Chart

Range

UCL

Rbar

LCL

0 2 4 6

Capability Plot

Data

Proc

Spec

0

0.2

0.4

0.6

0.8

1

1.2Individuals Plot

0.0000

0.2000

0.4000

0.6000

0.8000

1.0000

1.2000

1

The population distribution should be considered NORMAL.

Normal Probability Plot

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

0.

0000

Frequency

Bin

Histogram

F311.1 - Revised, GE, 31Aug05 Printed 12/20/2013 Printed copies are uncontrolled documents and may not be current. Page 2 of


3/18

Data Values Average Upper Spec Lower Spec % Z Ordered Data Statistic

# Data Poin

US

Targ

LS

Total Tolerancmea

media

Standard Deviatio

Upper Proc. Lim

Lower Proc. Lim

6 Sigm

C

C

Cp

C

Cp

Skewnes

Kurtos

Slop

InterceZ(US

Z(LS

% Over US

%Under LS

PPM Over US

PPM Under LS

PPM Tot

Shapiro-Wilks Norm

k

W

A2(Critical W)

Normal

Evaluation


4/18

Johnson Transformation Calculations for Standard CS (raw data):

Cumulative Probabilities Chart Val unbounded bounded lognormal

z 0.524 h

P(-3z) 0.058 g

P(-z) 0.300 l

P(z) 0.700 e

P(3z) 0.942 Data is Normal

Upper Proc. Bnd (Up)

Sample Percentiles Lower Proc. Bnd (Lp)

x(-3z) Median Target Value

x(-z) Cp

x(z) Cr

x(3z) Cpu

Cpl

Johnson Curve Cpk

m Z(USL)

n Z(LSL)

p % Over USL

mn/p2 % Under LSL

type PPM Over USL

PPM Under LSL

PPM Total

F311.1


5/18

Histogram Data

Raw Data Raw Data

bin 1 bin 2 bin 3 bin 4 bin 5 bin 6 bin 7 bin 8 bin 9 bin 10

Data Points 0

Range (R) 0.0000

Classes (K) 10

Class Width 0.0000

Bin NormDist Frequency Z

0.0000

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000 0

0.0000

0

Z Values

Norm Jns Su Jns Sb Jns Sl

Normsdist Values

Norm Jns Su Jns Sb Jns Sl

F311.1 Page 5


6/18

Subgroup Data Range Control Chart

SG 3 Piece 4 Piece 5 Piece SG Range UCL Rbar LCL

# Range X bar Range X bar Range X bar

1

2

3

4

5

6

7

8

9

10

11

12

13 In Control = Yes

R bar X bar bar R bar X bar bar R bar X bar bar

Constants Table Statistics

n D3 D4 A2 d2 n 3

2 0.000 3.267 1.880 1.128 R bar

3 0.000 2.574 1.023 1.693 UCL R

4 0.000 2.282 0.729 2.059 LCL R

5 0.000 2.114 0.577 2.326 X bar bar

UCL X bar

LCL X bar

A2*Rbar

numsubg 0


7/18

Shapiro-Wilk normality test. Calculation of W and comparison to critical value.

W = b / S if n is even, n = 2k; b = an(yn-y1) + an-1(yn-1-y2) + ak+1(yk+1-yk)

if n is odd, n = 2k - 1 ; b = an(yn-y1) + an-1(yn-1-y2) + ak+2(yk+2-yk)

y are the ordered (smallest to largest) data values

a are factors tabled in the SW Tables tab of this workbook

S is the sum of squares of y; S2= (y1-ybar)

2+ (y2-ybar)

2+ +(yn-ybar)

2

The SW test is a lower tail test. Small values indicate non-normality.

b =

S2= 95% Confidence Level

W = W0.95 =

n = 0

k

Data Values

Ordered L

to S

ata

Values

Ordered

S to L yn-i+1-yi

Tabled

Value of

an-i+1

F311.1


8/18

Tables from Shapiro and Wilk, Biometrika , Vol 52, pp 591-611.

i \ n 2 3 4 5 6 7 8 9

1 0.7071 0.7071 0.6872 0.6646 0.6431 0.6233 0.6052 0.5888

2 0.0000 0.1677 0.2413 0.2806 0.3031 0.3164 0.3244

3 0.0000 0.0875 0.1401 0.1743 0.1976

4 0.0000 0.0561 0.0947

5 0.0000

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

Percentage points of the W test* for n = 3(1)50

\ p 0.99 0.98 0.95 0.90 0.50 0.10 0.05 0.02

n \ (1-p) 0.01 0.02 0.05 0.10 0.50 0.90 0.95 0.98

3 0.753 0.756 0.767 0.789 0.959 0.998 0.999 1.000

4 0.687 0.791 0.748 0.792 0.935 0.987 0.992 0.996

5 0.686 0.715 0.762 0.806 0.927 0.979 0.986 0.991

6 0.713 0.743 0.788 0.826 0.927 0.974 0.981 0.986

7 0.730 0.760 0.803 0.838 0.928 0.972 0.979 0.985

8 0.749 0.778 0.818 0.851 0.932 0.972 0.978 0.984

9 0.764 0.791 0.829 0.859 0.935 0.972 0.978 0.984

10 0.781 0.806 0.842 0.869 0.938 0.972 0.978 0.983

11 0.792 0.817 0.850 0.876 0.940 0.973 0.979 0.984

12 0.805 0.828 0.859 0.883 0.943 0.973 0.979 0.984

13 0.814 0.837 0.866 0.889 0.945 0.974 0.979 0.984

14 0.825 0.846 0.874 0.895 0.947 0.975 0.980 0.984

15 0.835 0.855 0.881 0.901 0.950 0.975 0.980 0.984

F311.1


9/18

16 0.844 0.863 0.887 0.906 0.952 0.976 0.981 0.985

17 0.851 0.869 0.892 0.910 0.954 0.977 0.981 0.985

18 0.858 0.874 0.897 0.914 0.956 0.978 0.982 0.986

19 0.863 0.879 0.901 0.917 0.957 0.978 0.982 0.986

20 0.868 0.884 0.905 0.920 0.959 0.979 0.983 0.986

21 0.873 0.888 0.908 0.923 0.960 0.980 0.983 0.987

22 0.878 0.892 0.911 0.926 0.961 0.980 0.984 0.987

23 0.881 0.895 0.914 0.928 0.962 0.981 0.984 0.987

24 0.884 0.898 0.916 0.930 0.963 0.981 0.984 0.987

25 0.888 0.901 0.918 0.931 0.964 0.981 0.985 0.988

26 0.891 0.904 0.920 0.933 0.965 0.982 0.985 0.988

27 0.894 0.906 0.923 0.935 0.965 0.982 0.985 0.988

28 0.896 0.908 0.924 0.936 0.966 0.982 0.985 0.988

29 0.898 0.910 0.926 0.937 0.966 0.982 0.985 0.988

30 0.900 0.912 0.927 0.939 0.967 0.983 0.985 0.988

31 0.902 0.914 0.929 0.940 0.967 0.983 0.986 0.988

32 0.904 0.915 0.930 0.941 0.968 0.983 0.986 0.988

33 0.906 0.917 0.931 0.942 0.968 0.983 0.986 0.989

34 0.908 0.919 0.933 0.943 0.969 0.983 0.986 0.989

35 0.910 0.920 0.934 0.944 0.969 0.984 0.986 0.989

36 0.912 0.922 0.935 0.945 0.970 0.984 0.986 0.989

37 0.914 0.924 0.936 0.946 0.970 0.984 0.987 0.989

38 0.916 0.925 0.938 0.947 0.971 0.984 0.987 0.989

39 0.917 0.927 0.939 0.948 0.971 0.984 0.987 0.989

40 0.919 0.928 0.940 0.949 0.972 0.985 0.987 0.989

41 0.920 0.929 0.941 0.950 0.972 0.985 0.987 0.989

42 0.923 0.930 0.942 0.951 0.972 0.985 0.987 0.989

43 0.924 0.932 0.943 0.951 0.973 0.985 0.987 0.990

44 0.925 0.933 0.944 0.952 0.973 0.985 0.987 0.990

45 0.926 0.934 0.945 0.953 0.973 0.985 0.988 0.990

46 0.927 0.935 0.945 0.953 0.974 0.985 0.988 0.990

47 0.928 0.936 0.946 0.954 0.974 0.985 0.988 0.990

48 0.929 0.937 0.947 0.954 0.974 0.985 0.988 0.990

49 0.929 0.937 0.947 0.955 0.974 0.985 0.988 0.99050 0.930 0.938 0.947 0.955 0.974 0.985 0.988 0.990

* Based on fitted Johnson (1949) SBapproximation, see Shapiro and Wilk (Biometrika 1965) for details

F311.1


10/18

10 11 12 13 14 15 16 17 18

0.5739 0.5601 0.5475 0.5359 0.5251 0.5150 0.5056 0.4968 0.4486

0.3291 0.3315 0.3325 0.3325 0.3318 0.3306 0.3290 0.3273 0.3253

0.2141 0.2260 0.2347 0.2412 0.2460 0.2495 0.2521 0.2540 0.2553

0.1224 0.1429 0.1586 0.1707 0.1802 0.1878 0.1939 0.1988 0.2027

0.0399 0.0695 0.0922 0.1099 0.1240 0.1353 0.1477 0.1524 0.1587

0.0000 0.0303 0.0539 0.0727 0.0880 0.1005 0.1109 0.1197

0.0000 0.0240 0.0433 0.0593 0.0725 0.0837

0.0000 0.0196 0.0359 0.0496

0.0000 0.0163

0.01

0.99

1.000

0.997

0.993

0.989

0.988

0.987

0.986

0.986

0.986

0.986

0.986

0.986

0.987

F311.1


11/18


12/18

Coefficients {an-i+1} for the W test for normality for n = 2(1)50

19 20 21 22 23 24 25 26 27

0.4808 0.4734 0.4643 0.4590 0.4542 0.4493 0.4450 0.4407 0.4366

0.3232 0.3211 0.3185 0.3156 0.3126 0.3098 0.3069 0.3403 0.3018

0.2561 0.2565 0.2578 0.2571 0.2563 0.2554 0.2543 0.2533 0.2522

0.2059 0.2085 0.2119 0.2131 0.2139 0.2145 0.2148 0.2151 0.2152

0.1641 0.1686 0.1736 0.1764 0.1787 0.1807 0.1822 0.1836 0.1848

0.1271 0.1334 0.1399 0.1443 0.1480 0.1512 0.1539 0.1563 0.1584

0.0932 0.1013 0.1092 0.1150 0.1201 0.1245 0.1283 0.1316 0.1346

0.0612 0.0711 0.0804 0.0878 0.0941 0.0997 0.1046 0.1089 0.1128

0.0303 0.0422 0.0530 0.0618 0.0696 0.0764 0.0823 0.0876 0.0923

0.0000 0.0140 0.0263 0.0368 0.0459 0.0539 0.0601 0.0672 0.0728

0.0000 0.0122 0.0228 0.0321 0.0403 0.0476 0.0540

0.0000 0.0107 0.0200 0.0284 0.0358

0.0000 0.0094 0.0178

0.0000

F311.1


13/18

F311.1


14/18


15/18

F311.1


16/18


17/18

F311.1


18/18

46 47 48 49 50

0.3830 0.3808 0.3789 0.3770 0.3751

0.2635 0.2620 0.2604 0.2589 0.2574

0.2302 0.2291 0.2281 0.2271 0.2260

0.2058 0.2052 0.2045 0.2038 0.2032

0.1862 0.1859 0.1855 0.1851 0.1847

0.1695 0.1695 0.1693 0.1692 0.1619

0.1548 0.1550 0.1551 0.1553 0.1554

0.1415 0.1420 0.1423 0.1427 0.1430

0.1293 0.1300 0.1306 0.1312 0.1317

0.1180 0.1189 0.1197 0.1205 0.1212

0.1073 0.1085 0.1095 0.1105 0.1113

0.0972 0.0986 0.0998 0.1010 0.1020

0.0876 0.0892 0.0906 0.0919 0.0932

0.0783 0.0801 0.0817 0.0832 0.0846

0.0694 0.0713 0.0731 0.0748 0.0764

0.0607 0.0628 0.0648 0.0667 0.0685

0.0522 0.0546 0.0568 0.0588 0.0608

0.0439 0.0465 0.0489 0.0511 0.0532

0.0357 0.0385 0.0411 0.0436 0.0459

0.0277 0.0307 0.0335 0.0361 0.0386

0.0197 0.0229 0.0259 0.0288 0.0314

0.0118 0.0153 0.0185 0.0215 0.0244

0.0039 0.0076 0.0111 0.0143 0.0174

0.0000 0.0037 0.0071 0.0104

0.0000 0.0035

F311 1

Documents

F311_1CapStudyTemplate